%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL580^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:23 AM UTC 2026
% Result : Theorem 0.27s 0.33s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 21 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 100 ( 7 ~; 0 |; 0 &; 73 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 33 usr; 5 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 40 ( 36 ^; 4 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
r: $i > $i > $o ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
vOR: $o > $o > $o ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
vIMP: $o > $o > $o ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(f2,axiom,
( ( ^ [X0: $i] : $true )
= mtrue ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mtrue) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,conjecture,
mvalid @ ( mbox @ r @ mtrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f17,negated_conjecture,
~ ( mvalid @ ( mbox @ r @ mtrue ) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
thf(f18,plain,
~ ( mvalid @ ( mbox @ r @ mtrue ) ),
inference(rectify,[],[f17]) ).
thf(f19,plain,
( ( mvalid @ ( mbox @ r @ mtrue ) )
!= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f22,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f23,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f36,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(fool_elimination,[],[f2]) ).
thf(f42,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f43,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f46,plain,
( ( mvalid @ ( mbox @ r @ mtrue ) )
!= $true ),
inference(flattening,[],[f19]) ).
thf(f48,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f55,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f57,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f59,plain,
( ( mvalid @ ( mbox @ r @ mtrue ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f67,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ ^ [Y0: $i] : $true ) ) ),
inference(definition_unfolding,[],[f59,f57,f55,f48]) ).
thf(f68,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> $true ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f67]) ).
thf(f69,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> $true ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> $true ) )
= $false ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
( ( ^ [Y0: $i] :
( ( r @ sK0 @ Y0 )
=> $true )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f70]) ).
thf(f72,plain,
( ( ( r @ sK0 @ sK1 )
=> $true )
= $false ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
$true = $false,
inference(imp_proxy_clausification,[],[f72]) ).
thf(f75,plain,
$false,
inference(trivial_inequality_removal,[],[f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL580^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n011.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 08:55:01 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 Running higher-order theorem proving
% 0.10/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.33 % (4021060)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.27/0.33 % (4021069)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1414533041:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.27/0.33 % (4021066)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1754278471:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.27/0.33 % (4021066) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4021060-4021066"...
% 0.27/0.33 % (4021066)...printing done.
% 0.27/0.33 % (4021066)Refutation found. Thanks to Tanya!
% 0.27/0.33 % SZS status Theorem for theBenchmark
% 0.27/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.33 % (4021066)------------------------------
% 0.27/0.33 % (4021066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.33 % (4021066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.33 % (4021066)CaDiCaL version: 2.1.3
% 0.27/0.33 % (4021066)Termination reason: Refutation
% 0.27/0.33 % (4021066)Time elapsed: 0.003 s
% 0.27/0.33 % (4021066)Peak memory usage: 12 MB
% 0.27/0.33 % (4021066)Instructions burned: 3 (million)
% 0.27/0.33 % (4021060)Success in time 0.029 s
% 0.27/0.33 % Vampire exiting
%------------------------------------------------------------------------------